The “sonic distance” between two notes is called an interval. If the notes are sounded consecutively, we call it a melodic interval (or “horizontal”); if simultaneously, a harmonic (or “vertical”) one. The naming of the intervals is somewhat odd, being based on the total number of lines and spaces included by the notes when they are written on a music staff. So, the interval between the notes C and D is a “second”, between C and E a “third”, etc. Because you are counting both “end points”, when you add two intervals together, you have to subtract one from the sum, because you have counted the note that is the end of the first interval and the start of the second twice. Clearly, this is not the most untuitively friendly system, but we are stuck with it. The easiest way to understand it is visually, so let’s go back to the chromatic scale we derived last week:

c c# d d# e f f# g g# a a# b c db eb gb ab bb

On our “Bluegrass piano”, the notes without sharp/flat symbols are the white keys, the others the black keys. The basic name of the interval depends on the names of the notes, without regard to any sharp or flat. So, c to d is a second, as is c to db or c to d#. Oh, oh! This implies that seconds come in different sizes, and they do, as do all intervals. Recall that last month we defined a “semitone” as the sonic distance between adjacent keys on the piano (whether black or white) or between two frets on a guitar, mandolin or banjo. We can define each interval and its types in terms of the number of semitones:

#semitones interval name example0 perfect unison c to c1 minor second c to db2 major second c to d3 minor third c to eb4 major third c to e5 perfect fourth c to f6 augmented fourth c to f#6 diminished fifth c to gb7 perfect fifth c to g8 minor sixth c to ab9 major sixth c to a10 minor seventh c to bb11 major seventh c to b12 perfect octave c to c above

Now we can relate these intervals to the major scale we derived last month. Measuring from the “key note”, a major scale consists of:

c to d – major secondc to e – major thirdc to f – perfect fourthc to g – perfect fifthc to a – major sixthc to b – major seventhc to c – perfect octave

Remember that EVERY major scale consists of these intervals, no matter on which note you begin. However, when you start on a note other than c, you are going to have to deal with those pesky black keys, the sharps or flats. What if we start the scale on g instead of c? Then we will have:

g to a – major secondg to b – major thirdg to c – perfect fourthg to d – perfect fifthg to e – major sixthg to ???????? – major seventh

Careful, here. We know a major seventh is 11 semitones wide (or high, as the case may be), but if we rearrange our chromatic scale to begin with g and count, we find that g to f is only 10 semitones:

g g# a a# b c c# d d# e f f#

So, in the major scale on g, the seventh note is f#, not f. This is the only note different from the major scale on c. There is a neat little secret hiding under here, but we need a little more terminology (sorry!) to uncover it. Let’s name the “degrees” of our scale:

1 tonic2 supertonic3 mediant (halfway from tonic to dominant)4 subdominant (as far below the tonic as the dominant in above it)5 dominant6 submediant (halfway down from tonic to subdominant)7 leading tone

In Bluegrass, we generally only use the terms for the 1st, 4th and 5th degrees of the scale. Given that, the “secret” is this:

Starting from C major, with no sharps or flats, when you go to the key of the dominant, you sharp the subdominant of the first key, which will be the leading tone (7th degree) of the new key. You can keep doing this, around what is called the “Circle of Fifths”, keeping any notes already sharped. Let’s see how this plays out:

That’s as far as we need to go for Bluegrass. But what about going in the other direction? What about the key of F, for example?

f f# g g# a a# b c c# d d# e g gb ab bb db eb

Let’s try f g a b c d e f. Wait, we know that we need a perfect fourth up from the tonic for the subdominant, five semitones, but f to b is six semitones, so we need one semitone lower; we already have ‘a’, a major third above f, so we don’t want to call it ‘a#’, so we need “bb” (b flat). So, the alternate rule is:

Starting from C major, with no sharps or flats, when you go to the key of the subdominant, you flat the leading tone (7th degree) of the first key, which will be the subdominant (4th degree) of the new key. You can keep doing this, around what is called the “Circle of Fourths”, keeping any notes already flatted. Let’s see how this plays out:

c – no sharps or flatsf – bbbb – bb, ebeb – bb, eb, ab

In Bluegrass, you generally do not find tunes in eb or “flatter” keys.

Next week – chords!!!

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